## Calculus (3rd Edition)

The function is discontinuous at every $x=n$. The discontinuity here is a jump discontinuity. Moreover, the function is left continuous.
We know that the function $[x]$ has a jump discontinuity and is left continuous at $x=n$. Thus, the function $$\cos \pi[x]$$ is discontinuous at every $x=n$. The discontinuity here is a jump discontinuity. Moreover, the function is left continuous.